BEE Signals & Systems 4

Question 1

The convolution of u(t) with itself, u(t) * u(t), results in:

Accepted Answer

t·u(t)

Answer

Convolving two unit step functions yields the ramp signal r(t) = t·u(t).

Question 2

The power spectral density (PSD) of a wide-sense stationary (WSS) random process is the Fourier transform of its:

Accepted Answer

Autocorrelation function

Answer

By the Wiener-Khinchin theorem, the PSD is the Fourier transform of the autocorrelation function.

Question 3

A system is memoryless if its output at time t depends only on:

Accepted Answer

The input at the same instant t

Answer

A memoryless system's output depends solely on the present input value, with no dependency on past or future.

Question 4

The Laplace transform of the unit ramp r(t) = t·u(t) is:

Accepted Answer

1/s²

Answer

L{t·u(t)} = 1/s², valid for Re{s} > 0.

Question 5

Gibb's phenomenon occurs when reconstructing a signal from its Fourier series near a:

Accepted Answer

Discontinuity

Answer

Gibbs phenomenon produces approximately 9% overshoot near jump discontinuities regardless of how many harmonics are included.

BEE - Bachelor of Electrical Engineering Practice Test